J. Ponce de Leon1

Abstract

A striking characteristic of non-Schwarzschild vacuum exteriors is that they contain not only the total gravitational mass of the source but also an arbitrary constant. In this work, we show that the constants appearing in the "temporal Schwarzschild", ßpatial Schwarzschild" and "Reissner-Nordström-like" exteriors are not arbitrary but are completely determined by the star's parameters, like the equation of state and the gravitational potential. Consequently, in the braneworld scenario, the gravitational field outside a star is no longer determined by the total mass alone but also depends on the details of the internal structure of the source. We show that the general-relativistic upper bound on the gravitational potential M/R < 4/9 for perfect fluid stars is significantly increased in these exteriors. Namely, M/R < 1/2, M/R < 2/3 and M/R < 1 for the temporal Schwarzschild, spatial Schwarzschild and Reissner-Nordström-like exteriors, respectively. We find that stellar models embedded in such exteriors are very diverse and rich in structure: For stars like our Sun, the deviation from the Schwarzschild exterior metric is automatically negligible, but in other limits they allow the existence of new kinds of stellar models which have no general-relativistic counterpart. Regarding the surface gravitational redshift, we find that the general-relativistic Schwarzschild exterior as well as the braneworld spatial Schwarzschild exterior lead to the same upper bound, viz., Z < 2. However, when the external spacetime is the temporal Schwarzschild metric or the Reissner-Nordström-like exterior, there is no such constraint: Z < ¥. This infinite difference in the limiting value of Z is because for these exteriors the effective pressure at the surface is negative. The results of our work are potentially observable and can be used to test the theory.